'The total return on a portfolio of investments takes into account not only the capital appreciation on the portfolio, but also the income received on the portfolio. The income typically consists of interest, dividends, and securities lending fees. This contrasts with the price return, which takes into account only the capital gain on an investment.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (95%) in the period of the last 5 years, the total return of 829.7% of ProShares UltraPro QQQ is higher, thus better.
- During the last 3 years, the total return is 244.9%, which is greater, thus better than the value of 40.5% from the benchmark.

'Compound annual growth rate (CAGR) is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the time period. CAGR is not an accounting term, but it is often used to describe some element of the business, for example revenue, units delivered, registered users, etc. CAGR dampens the effect of volatility of periodic returns that can render arithmetic means irrelevant. It is particularly useful to compare growth rates from various data sets of common domain such as revenue growth of companies in the same industry.'

Which means for our asset as example:- Looking at the compounded annual growth rate (CAGR) of 56.2% in the last 5 years of ProShares UltraPro QQQ, we see it is relatively higher, thus better in comparison to the benchmark SPY (14.3%)
- Looking at compounded annual growth rate (CAGR) in of 51.2% in the period of the last 3 years, we see it is relatively greater, thus better in comparison to SPY (12%).

'Volatility is a statistical measure of the dispersion of returns for a given security or market index. Volatility can either be measured by using the standard deviation or variance between returns from that same security or market index. Commonly, the higher the volatility, the riskier the security. In the securities markets, volatility is often associated with big swings in either direction. For example, when the stock market rises and falls more than one percent over a sustained period of time, it is called a 'volatile' market.'

Applying this definition to our asset in some examples:- Looking at the 30 days standard deviation of 64.1% in the last 5 years of ProShares UltraPro QQQ, we see it is relatively larger, thus worse in comparison to the benchmark SPY (18.8%)
- Compared with SPY (22.4%) in the period of the last 3 years, the historical 30 days volatility of 75.1% is higher, thus worse.

'The downside volatility is similar to the volatility, or standard deviation, but only takes losing/negative periods into account.'

Which means for our asset as example:- The downside deviation over 5 years of ProShares UltraPro QQQ is 46.2%, which is greater, thus worse compared to the benchmark SPY (13.7%) in the same period.
- Compared with SPY (16.5%) in the period of the last 3 years, the downside deviation of 54.4% is greater, thus worse.

'The Sharpe ratio was developed by Nobel laureate William F. Sharpe, and is used to help investors understand the return of an investment compared to its risk. The ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk. Subtracting the risk-free rate from the mean return allows an investor to better isolate the profits associated with risk-taking activities. One intuition of this calculation is that a portfolio engaging in 'zero risk' investments, such as the purchase of U.S. Treasury bills (for which the expected return is the risk-free rate), has a Sharpe ratio of exactly zero. Generally, the greater the value of the Sharpe ratio, the more attractive the risk-adjusted return.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (0.63) in the period of the last 5 years, the ratio of return and volatility (Sharpe) of 0.84 of ProShares UltraPro QQQ is higher, thus better.
- Compared with SPY (0.43) in the period of the last 3 years, the ratio of return and volatility (Sharpe) of 0.65 is higher, thus better.

'The Sortino ratio, a variation of the Sharpe ratio only factors in the downside, or negative volatility, rather than the total volatility used in calculating the Sharpe ratio. The theory behind the Sortino variation is that upside volatility is a plus for the investment, and it, therefore, should not be included in the risk calculation. Therefore, the Sortino ratio takes upside volatility out of the equation and uses only the downside standard deviation in its calculation instead of the total standard deviation that is used in calculating the Sharpe ratio.'

Applying this definition to our asset in some examples:- Looking at the excess return divided by the downside deviation of 1.16 in the last 5 years of ProShares UltraPro QQQ, we see it is relatively greater, thus better in comparison to the benchmark SPY (0.86)
- Compared with SPY (0.58) in the period of the last 3 years, the ratio of annual return and downside deviation of 0.9 is greater, thus better.

'The Ulcer Index is a technical indicator that measures downside risk, in terms of both the depth and duration of price declines. The index increases in value as the price moves farther away from a recent high and falls as the price rises to new highs. The indicator is usually calculated over a 14-day period, with the Ulcer Index showing the percentage drawdown a trader can expect from the high over that period. The greater the value of the Ulcer Index, the longer it takes for a stock to get back to the former high.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (5.79 ) in the period of the last 5 years, the Ulcer Index of 19 of ProShares UltraPro QQQ is higher, thus worse.
- During the last 3 years, the Ulcer Ratio is 23 , which is larger, thus worse than the value of 7.09 from the benchmark.

'Maximum drawdown measures the loss in any losing period during a fund’s investment record. It is defined as the percent retrenchment from a fund’s peak value to the fund’s valley value. The drawdown is in effect from the time the fund’s retrenchment begins until a new fund high is reached. The maximum drawdown encompasses both the period from the fund’s peak to the fund’s valley (length), and the time from the fund’s valley to a new fund high (recovery). It measures the largest percentage drawdown that has occurred in any fund’s data record.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum DrawDown of -69.9 days of ProShares UltraPro QQQ is lower, thus worse.
- Looking at maximum DrawDown in of -69.9 days in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (-33.7 days).

'The Drawdown Duration is the length of any peak to peak period, or the time between new equity highs. The Max Drawdown Duration is the worst (the maximum/longest) amount of time an investment has seen between peaks (equity highs). Many assume Max DD Duration is the length of time between new highs during which the Max DD (magnitude) occurred. But that isn’t always the case. The Max DD duration is the longest time between peaks, period. So it could be the time when the program also had its biggest peak to valley loss (and usually is, because the program needs a long time to recover from the largest loss), but it doesn’t have to be'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (139 days) in the period of the last 5 years, the maximum time in days below previous high water mark of 296 days of ProShares UltraPro QQQ is larger, thus worse.
- Looking at maximum time in days below previous high water mark in of 296 days in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (139 days).

'The Drawdown Duration is the length of any peak to peak period, or the time between new equity highs. The Avg Drawdown Duration is the average amount of time an investment has seen between peaks (equity highs), or in other terms the average of time under water of all drawdowns. So in contrast to the Maximum duration it does not measure only one drawdown event but calculates the average of all.'

Which means for our asset as example:- Compared with the benchmark SPY (37 days) in the period of the last 5 years, the average days below previous high of 68 days of ProShares UltraPro QQQ is greater, thus worse.
- During the last 3 years, the average days below previous high is 80 days, which is greater, thus worse than the value of 45 days from the benchmark.

Historical returns have been extended using synthetic data.
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- Note that yearly returns do not equal the sum of monthly returns due to compounding.
- Performance results of ProShares UltraPro QQQ are hypothetical, do not account for slippage, fees or taxes, and are based on backtesting, which has many inherent limitations, some of which are described in our Terms of Use.